Abstract: Polymer sheets or films are provided with tear paths that are substantially indistinguishable from the remainder of the polymer sheet or film in outward appearance and in chemical properties. Throughout the tear path, molecular chains of the polymer are oriented generally along a predetermined axis, while the molecular chains of the remainder of the polymer sheet or film are oriented generally differently from said predetermined axis. Such tear paths are typically formed by means of a device that extracts heat from the polymer as it is extruded or otherwise molded, the extraction rate being faster than the rate at which the remainder of the molded polymer is cooled in order to encourage maintenance of the substantially monoaxial orientation of the polymer chains along the tear path when the entire polymer is subsequently blown up or otherwise reoriented.